a) $\left\{\begin{matrix}-2x+5y=9 & \\ 4x+2y=11 & \end{matrix}\right.$

<=> $\left\{\begin{matrix}-4x+10y=18 & \\ 4x+2y=11 & \end{matrix}\right.$

<=> $\left\{\begin{matrix}12y=29 & \\ 4x+2y=11 & \end{matrix}\right.$

<=> $\left\{\begin{matrix}y=\frac{29}{12} & \\ x=\frac{37}{24} & \end{matrix}\right.$

Vậy $\left\{\begin{matrix} x=\frac{37}{24} & \\ y=\frac{29}{12}& \end{matrix}\right.$.

b) $\left\{\begin{matrix}3x+4y=12 & \\ 5x-2y=7 & \end{matrix}\right.$

<=> $\left\{\begin{matrix}3x+4y=12 & \\ 10x-4y=14 & \end{matrix}\right.$

<=> $\left\{\begin{matrix}3x+4y=12 & \\ 13x=26 & \end{matrix}\right.$

<=> $\left\{\begin{matrix}x=2 & \\ y=\frac{3}{2} & \end{matrix}\right.$

Vậy $\left\{\begin{matrix}x=2 & \\ y=\frac{3}{2} & \end{matrix}\right.$

c) $\left\{\begin{matrix}2x-3y=5 & \\ 3x+2y=8 & \end{matrix}\right.$

<=> $\left\{\begin{matrix}4x-6y=10 & \\ 9x+6y=24 & \end{matrix}\right.$

<=> $\left\{\begin{matrix}4x-6y=10 & \\ 13x=34 & \end{matrix}\right.$

<=> $\left\{\begin{matrix}y=\frac{1}{13} & \\ x=\frac{34}{13} & \end{matrix}\right.$

Vậy $\left\{\begin{matrix}x=\frac{34}{13}& \\  y=\frac{1}{13} & \end{matrix}\right.$

d) $\left\{\begin{matrix}5x+3y=15 & \\ 4x-5y=6 & \end{matrix}\right.$

<=> $\left\{\begin{matrix}25x+15y=75 & \\ 12x-15y=18 & \end{matrix}\right.$

<=> $\left\{\begin{matrix}37x=93 & \\ 12x-15y=18 & \end{matrix}\right.$

<=> $\left\{\begin{matrix}x=\frac{93}{37} & \\ y=\frac{30}{37} & \end{matrix}\right.$

Vậy $\left\{\begin{matrix}x=\frac{93}{37} & \\ y=\frac{30}{37} & \end{matrix}\right.$